Question: Christopher is 3 times as old as Umaima. Eighteen years ago, Christopher was 9 times as old as Umaima. How old is Umaima now?
Answer: We can use the given information to write down two equations that describe the ages of Christopher and Umaima. Let Christopher's current age be $c$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $c = 3u$ Eighteen years ago, Christopher was $c - 18$ years old, and Umaima was $u - 18$ years old. The information in the second sentence can be expressed in the following equation: $c - 18 = 9(u - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 3u$ . Substituting this into our second equation, we get: $3u$ $-$ $18 = 9(u - 18)$ which combines the information about $u$ from both of our original equations. Simplifying the right side of this equation, we get: $3 u - 18 = 9 u - 162$ Solving for $u$ , we get: $6 u = 144.$ $u = 24$.